how to find the estimated simple linear regression equation

The variance in simple linear regression can be expressed as a relationship between the actual value, the fitted value, and the grand mean-all in terms of Y. Y: the dependent variable that we want to predict.X: the independent variable that we use to predict.The fitted value of the dependent variable:īy using calculus, it can be shown the sum of squared error is minimal when The actual value of the dependent variable: In mathematical language, we look for α and β that satisfy the following criteria: the vertical difference between the data point and the fitting line). It estimates the unknown parameters of the regression equation by minimizing the sum of squared residuals (i.e. The ordinary least squares is a statistical method used in linear regression analysis to find the best fitting line for the data points.

It is the difference between the actual Y and the fitted Y (i.e.

β is the intercept indicating the Y value when X is equal to 0

α is the slope describing the steepness of the fitting line.

Y is the dependent variable (the response) and X is the single independent variable (the predictor).

The simple linear regression analysis fits the data to a regression equation in the form Both variables need to be continuous there are other types of regression to model discrete data. It describes how one variable changes according to the change of another variable. It is simple because only one predictor variable is involved. It models the quantitative relationship between two variables. Simple linear regression is a statistical technique to fit a straight line through the data points.

How to find the estimated simple linear regression equation